Temperature-dependent thermal conductivity in silicon nanostructured materials studied by the Boltzmann transport equation

Nanostructured materials exhibit low thermal conductivity because of the additional scattering due to phononboundary interactions. As these interactions are highly sensitive to the mean free path (MFP) of phonons, MFP distributions in nanostructures can be dramatically distorted relative to bulk. Here we calculate the MFP distribution in periodic nanoporous Si for different temperatures, using the recently developed MFP-dependent Boltzmann transport equation. After analyzing the relative contribution of each phonon branch to thermal transport in nanoporous Si, we find that at room temperature optical phonons contribute 17% to heat transport, compared to 5% in bulk Si. Interestingly, we observe a constant thermal conductivity over the range 200 K < T < 300 K. We attribute this behavior to the ballistic transport of acoustic phonons with long intrinsic MFP and the temperature dependence of the heat capacity. Our findings, which are in qualitative agreement with the temperature trend of thermal conductivities measured in nanoporous Si-based systems, shed light on the origin of the reduction of thermal conductivity in nanostructured materials and demonstrate the necessity of multiscale heat transport engineering, in which the bulk material and geometry are optimized concurrently.